Choosing a manifold in state space parameterized by the orientation and strength of a magnetic field makes this study distinct from many other investigations of the many-body quantum state space geometry, which tend to employ state space manifolds parameterized by the driving parameters of the phase transitions (see, for example  [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, or by examining the geometry of the momentum bands in Fermion models (see [8]} for a very general treatment of \(N\)  level systems).
